Villaraigosa was referring to the number of prominent Hispanic Republicans slated to speak at the Republican National Convention this week, but Rubio said the mayor's message applies to both parties.

"I think what he's saying, quite frankly, is true for both parties," said Rubio, who spoke to me this morning on "Good Morning America." "Policies matter and, look, the Republican Party does have a challenge. We can't just be the anti-illegal immigration party, we have to be the pro-legal immigration party.

"We have a broken system of immigration that needs to be fixed and we have a legal immigration problem because we have millions of people who are in this country without documents and we have to deal with that in a way that honors our legacy both as a nation of compassion and a nation of immigrants but also as a nation of laws. That's a real challenge. That's not an easy thing to do. We're going to confront that not by pandering, not by making unrealistic promises but by trying to find a balanced approach to how to deal with it."

Recent polls show that Mitt Romney, the GOP nominee for president, is struggling with Latino voters. Hispanics are a growing minority in the United States and a key demographic in Rubio's home state of Florida, a crucial swing state in the presidential election. Romney has expressed views on immigration seen as being to the right of former President George W. Bush - who was for comprehensive immigration reform - while President Obama, who has much higher support among Latino voters, issued an executive order earlier this year that would allow some undocumented immigrants legal status.

Rubio told me this morning that Romney would replace this policy.

"I think he's going to replace it. That's what I think you can expect from the Romney presidency and I think the obligation of some of us in the Congress is to find that permanent solution," Rubio, 41, said. "It was something I was working on, that I continue to work on, an alternative to the DREAM Act that allows us to continue to deal with that issue but not in a way that's amnesty and not in a way that encourages illegal immigration in the future."

Rubio, who is Cuban-American, is among several Hispanic Republicans who have prominent roles at the Republican National Convention this week. Rubio will introduce Romney Thursday night on the final night of the convention in Tampa, Fla., before the former Massachusetts governor formally accepts the GOP nomination for president.

"I hope to present to the people of the United States in the few minutes that I have, two things. A very unique human being, Mitt Romney, who has lived his life in a way that's not just admirable but really a role model, irrespective of how people may feel about his policies, they may disagree with him on policies, but you look at the way he's lived his life as a husband, as a father, as a member of his community, really a role model for younger Americans and what we should all aspire for our kids to be," Rubio said.

"And then, also, the choice that America has between two very different views of government's role in our economy. That's really what this election is about. It's not just a choice between a Democrat and a Republican, it's a choice between two very different futures. I hope I can do that for him."